Don't gun shows allow you to buy when from a different state?
At the show here on the 19th, the seller asked me whether I'm a TN resident.

Under Federal law, you may purchase long guns ONLY (not handguns) in another state if (and only if) it is legal in both locations. In other words, it must be legal for you to be able to purchase long guns in your home state without benefit of 10 or 15 day waiting periods, etc., AND it must be legal in the state where the gun show is. It could also be the case where some local or state law in your home state might prohibit you from purchasing out of state, or the host state or municipality of the gun show may prohibit sales to out-of-staters.

Unfortunately, some FFL dealers are either ignorant of the Federal laws regarding this or just too paranoid to sell to an out-of-stater. In defense of the dealer, however, one can't know every law of every state.